A nonlinear generalization of spectral granger causality

IEEE Transactions on Biomedical Engineering

Volumn 61, Issue 6, 2014, Pages 1693-1701

  He, Fei ^a   Wei, Hua Liang ^a   Billings, Stephen A ^a   Sarrigiannis, Ptolemaios G ^b  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

^b ROYAL HALLAMSHIRE HOSPITAL   (United Kingdom)

Author keywords

Electroencephalogram (EEG); frequency response function (FRF); Granger causality; nonlinear systems; spectral analysis

Indexed keywords

ELECTROENCEPHALOGRAPHY; FREQUENCY RESPONSE; NONLINEAR SYSTEMS; SIGNAL PROCESSING; SPECTRUM ANALYSIS; TIME SERIES;

AUTOREGRESSIVE WITH EXOGENOUS INPUTS; BIVARIATE SIGNALS; ELECTRO-ENCEPHALOGRAM (EEG); FREQUENCY DOMAINS; FREQUENCY RESPONSE FUNCTIONS; GRANGER CAUSALITY; NONLINEAR CAUSALITIES; NONLINEAR GENERALIZATIONS;

STATISTICAL TESTS;

ARTICLE; CONTROLLED STUDY; ELECTROENCEPHALOGRAM; FOCAL EPILEPSY; FOURIER TRANSFORMATION; GRANGER CAUSALITY; HIPPOCAMPAL SCLEROSIS; HUMAN; NONLINEAR SYSTEM; POWER SPECTRUM; PREDICTION; SEIZURE; STATISTICAL MODEL; TEMPORAL LOBE EPILEPSY; TIME SERIES ANALYSIS; WHITE NOISE; ALGORITHM; ELECTROENCEPHALOGRAPHY; EPILEPSY; PATHOPHYSIOLOGY; PROCEDURES; SIGNAL PROCESSING;

ALGORITHMS; ELECTROENCEPHALOGRAPHY; EPILEPSY; HUMANS; NONLINEAR DYNAMICS; SIGNAL PROCESSING, COMPUTER-ASSISTED;

EID: 84901268752     PISSN: 00189294     EISSN: 15582531     Source Type: Journal    
DOI: 10.1109/TBME.2014.2300636     Document Type: Article

References (35)

1. C. Granger, "Investigating causal relations by econometric models and cross-spectral methods," Econometrica, vol. 37, pp. 424-438, 1969.
2. U. Soytas and R. Sari, "Energy consumption and GDP: Causality relationship in G-7 countries and emerging markets," Energy Econ., vol. 25, pp. 33-37, Jan. 2003. (Pubitemid 36036587)
3. B. He, L. Yang, C. Wilke, and H. Yuan, "Electrophysiological imaging of brain activity and connectivity - Challenges and opportunities," IEEE Trans. Biomed. Eng., vol. 58, no. 7, pp. 1918-1931, Jul. 2011.
4. M. Ding, Y. Chen, and S. Bressler, "Granger causality: Basic theory and application to neuroscience," in Handbook of Time Series Analysis, B. Schelter, M. Winterhalder, and J. Timmer, Eds. New York, NY, USA: Wiley, 2006, pp. 438-460.
5. A. Brovelli, M. Ding, A. Ledberg, Y. Chen, R. Nakamura, and S. L. Bressler, "Beta oscillations in a large-scale sensorimotor cortical network: Directional influences revealed by Granger causality," Proc Nat. Acad. Sci. USA, vol. 101, pp. 9849-9854, Jun. 2004. (Pubitemid 38869325)
6. A. K. Seth, "AMATLAB toolbox for Granger causality connectivity analysis," J. Neurosci. Methods, vol. 186, pp. 262-273, Feb. 2010.
7. C. Zou and J. Feng, "Granger causality vs. dynamic Bayesian network inference: A comparative study," BMC Bioinformat., vol. 10, pp. 122-138, Apr. 2009.
8. J. F. Feng, D. Y. Yi, R. Krishna, S. X. Guo, and V. Buchanan-Wollaston, "Listen to genes: Dealing with microarray data in the frequency domain," PLoS ONE, vol. 4, no. 4, p. e5098+, Apr. 2009.
9. D. Chicharro, "On the spectral formulation of granger causality," Biol. Cybern., vol. 105, no. 5/6, pp. 331-347, Dec. 2011.
10. J. Geweke, "Measurement of linear dependence and feedback between multiple time series," J. Amer. Statist. Assoc., vol. 77, pp. 304-313, 1982.
11. L. A. Baccal and K. sameshima, "Partial directed coherence: a newconcept in neural structure determination," Biol. Cybern, vol. 84, pp. 463-474, Jun. 2001. (Pubitemid 33605196)
12. M. J. Kaminski and K. J. Blinowska, "A new method of the description of the information-flow in the brain structures," Biol. Cybern, vol. 65, no. 3, pp. 203-210, 1991.
13. C. Wilke, L. Ding, and B. He, "Estimation of time-varying connectivity patterns through the use of an adaptive directed transfer function," IEEE Trans. Biomed. Eng., vol. 55, no. 11, pp. 2557-2564, Nov. 2008.
14. C. Wilke, W. vanDrongelen, M. Kohrman, and B. He, "Neocortical seizure foci localization bymeans of a directed transfer functionmethod," Epilepsia, vol. 51, no. 4, pp. 564-572, 2010.
15. Y. Lu, L. Yang, G. A. Worrell, and B. He, "Seizure source imaging by means of FINE spatio-temporal dipole localization and directed transfer function in partial epilepsy patients," Clin. Neurophysiol., vol. 123, pp. 1275-1283, 2012.
16. S. A. Billings and K. M. Tsang, "Spectral analysis for non-linear systems. Part II: Interpretation of non-linear frequency response functions," Mech. Syst. Signal Process., vol. 3, no. 4, pp. 341-359, 1989.
17. Z. Q. Lang and S. A. Billings, "Energy transfer properties of nonlinear systems in the frequency domain," Int. J. Control, vol. 78, no. 5, pp. 345-362, 2005. (Pubitemid 41663516)
18. C. Hiemstra and J. Jones, "Testing for linear and nonlinear Granger causality in the stock price-volume relation," J. Finance, vol. 49, pp. 1639-1664, 1994.
19. C. Diks and V. Panchenko, "A new statistic and practical guidelines for nonparametric granger causality testing," J. Econ. Dyn. Control, vol. 30, pp. 1647-1669, Sep./Oct. 2006. (Pubitemid 44041167)
20. N. Ancona, D. Marinazzo, and S. Stramaglia, "Radial basis function approach to nonlinear granger causality of time series," Phys. Rev. E, vol. 70, p. 056221, Nov. 2004.
21. D. Marinazzo, M. Pellicoro, and S. Stramaglia, "Kernel Granger causality and the analysis of dynamical networks," Phys. Rev. E, vol. 77, p. 056215, May 2008.
22. Y. H. Chen, G. Rangarajan, J. F. Feng, and M. Z. Ding, "Analyzing multiple nonlinear time series with extended Granger causality," Phys. Lett. A, vol. 324, pp. 26-35, Apr. 5 2004.
23. Y. Li, H. L. Wei, S. A. Billings, and X. F. Liao, "Time-varying linear and nonlinear parametric model for Granger causality analysis," Phys. Rev. E, vol. 85, p. 041906, Apr. 2012.
24. Y. Zhao, S. A. Billings, H. L. Wei, F. He, and P. G. Sarrigiannis, "A new NARX-based granger linear and nonlinear casual influence detection method with applications to EEG data," J. Neurosci. Methods, vol. 212, pp. 79-86, Jan. 2013.
25. S. A. Billings, Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains. New York, NY, USA: Wiley, 2013.
26. S. Chen, S. A. Billings, and W. Luo, "Orthogonal least squares methods and their application to nonlinear system identification," Int. J. Control., vol. 50, no. 5, pp. 1873-1896, 1989. (Pubitemid 20636409)
27. S. A. Billings and W. S. E. Voon, "Structure detection and model validity test in the identification of nonlinear systems," IEE Proc., Pt. D: Control Theory Appl., vol. 130, pp. 193-199, 1983. (Pubitemid 13571064)
28. C. Gourierous and A. Monfort, Time Series and Dynamic Models. Cambridge, MA, U.K.: Cambridge Univ. Press, 1997.
29. Z. Q. Lang and S. A. Billings, "Output frequency characteristics of nonlinear systems," Int. J. Control, vol. 64, pp. 1049-1067, 1996. (Pubitemid 126519437)
30. J. C. Peyton Jones and S. A. Billings, "A recursive algorithm for computing the frequency response of a class of nonlinear difference equation models," Int. J. Control, vol. 50, no. 5, pp. 1925-1940, 1989. (Pubitemid 20636411)
31. S. L. Kukreja, H. L. Galiana, and R. E. Kearney, "NARMARX representation and identification of ankle dynamics," IEEE Trans. Biomed. Eng., vol. 50, no. 1, pp. 70-81, Jan. 2003. (Pubitemid 36227940)
32. C. J. Stam, "Nonlinear dynamical analysis of EEG and MEG: Review of an emerging field," Clin. Neurophysiol., vol. 116, pp. 2266-2301, 2005. (Pubitemid 41268636)
33. F. He, S. A. Billings, H. L. Wei, P. G. Sarrigiannis, and Y. Zhao, "Spectral analysis for nonstationary and nonlinear systems: A discrete-time-modelbased approach," IEEE Trans. Biomed. Eng., vol. 60, no. 8, pp. 2233-2241, Aug. 2013.
34. A. K. Swain and S. A. Billings, "Generalized frequency response function matrix for MIMO non-linear systems," Int. J. Control, vol. 74, pp. 829-844, May 2001.
35. A. B. Barrett, L. Barnett, and A. K. Seth, "Multivariate granger casuality and generalized variance," Phys. Rev. E, vol. 81, p. 041907, Apr. 2010.